Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 47

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Weekly Quiz Competition

Question 1
1 / -0

Some amount of water is poured on top face of a horizontal glass place. Excess amount of water spills over the edge a little amount of water there in a thin uniform layer a portion of which is shown in the figure. Surface tension of water is $$\sigma $$ the vertical thickness of the water layer far away the edge is t, the point in the plane on the diagram on the liquid where the liquid protrudes the most is D. The vertical depth of this point from the horizontal free surface of the water layer is d, p is density of water and g is acceleration due to gravity. Mark the correct relation(s)

A
$$t = \sqrt { \dfrac { 2 \sigma ( 1 + \sin \theta ) } { \rho g } }$$

B
$$t = \sqrt { \dfrac { 2 \sigma ( 1 - \cos \theta ) } { \rho g } }$$

C
$$d = \sqrt { \dfrac { 2 \sigma } { \rho g } }$$

D
$$d = \sqrt { \dfrac { 2 \sigma ( 1 - \cos \theta ) } { p g } }$$
Question 2
1 / -0

Air is streaming past a horizontal air plane wing such that its speed in 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per $$metre^3$$ and the wing is 1o m long and has an average width of 2m , then the difference of the pressure on the two sides of the wing of

A
4095.0 Pascal

B
409.50 Pascal

C
40.950 Pascal

D
4.0950 Pascal

Solution

Using the Bernoulli's theorem in the upper and lower surface of the wings in the airplane
$$ P_{1}-P_{2}=\dfrac{1}{2} \rho\left(v_{2}^{2}-v_{1}^{2}\right)$$

$$=\dfrac{1}{2} \times 1.3 \times\left[(120)^{2}-(90)^{2}\right] $$

$$ =4095 \mathrm{N} / \mathrm{m}^{2} $$ or Pascal
Question 3
1 / -0

The apparent depth of water in a cylindrical water tank of diameter $$2R$$ cm is reducing at the rate of $$x$$ cm/min when water is being drained out at a constant rate. The amount of water drained in $$cc/minute$$ is: ($${n_1}$$ = refractive index of air, $${n_2}$$ = refractive index of water)

A
$$\dfrac{{x\pi {R^2}{n_1}}}{{{n_2}}}$$

B
$$\dfrac{{x\pi {R^2}{n_2}}}{{{n_1}}}$$

C
$$\dfrac{{2\pi {R^{}}{n_1}}}{{{n_2}}}$$

D
$$\pi {R^2}x$$

Solution

We know that
$$\dfrac{Real Depth}{Apparent\ depth}=\dfrac{{n}_{2}}{{n}_{1}}$$
$$\Rightarrow \ $$Real Depth$$=\left(\dfrac{{n}_{2}}{{n}_{1}}\right)$$ Apparent Depth
Rate of change in real depth $$=\left(\dfrac{{n}_{2}}{{n}_{1}}\right)$$ rate of change in apparent depth
$$=\left(\dfrac{{n}_{2}}{{n}_{1}}\right)x$$
$$\dfrac{dv}{dt}=\dfrac{d\left(A\right)h}{dt}=\dfrac{Adh}{dt}=\left[n{\left(R\right)}^{2}\right]\left[\dfrac{{n}_{2}}{{n}_{1}}x\right]$$
Option $$B$$ is correct
Question 4
1 / -0

What principle law explains the working of the hydraulic brakes in automobiles?

A
Bernoulli's Law

B
Posieulles principle

C
Pascal's law

D
Archimedes principle

Solution

Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
Question 5
1 / -0

A cylindrical tank$$ I m$$ in radius rests on a platform$$ S m$$ high water,initially the tank is filled with water upto a height of $$ S m$$. A v.mg whose area is $$ 10 ^ { 4 } m ^ { 2 }$$is removed from an office on the side of the tank at the bottom .Calculate

A
initial speed with which the water flows from the orifice.

B
initial speed with which the water strikes the ground and

C
time taken to empty the tank to half its original value.

D
Does the time to empty the tank upon the height of stand?
Question 6
1 / -0

Find the depression of the meniscus in the capillary tube of diameter $$0.4\ mm$$, dipped in a beaker containing mercury. (Density of mercury $$=13.6\times 10^{3}\ kg/m^{3}$$) ; surface tension of the mercury is $$0.49\ N/m$$ ; angle of contact is $$135^{o}$$ ).

A
$$0.025\ cm$$

B
$$0.021\ cm$$

C
$$0.020\ cm$$

D
$$0.027\ cm$$

Solution

$$\text { We know that } \\$$

$$h =\left|\frac{2 T \cos \theta}{\rho g r}\right| \\$$

$$H =\frac{2 \times 0.49 \times 1 / \sqrt{2}}{13.6 \times 10^{3} \times 10 \times 0.2 \times 10^{-3}}=0.025 \mathrm{~cm} \\$$

$$ \text { Answerl:- (A) } 0.025 \mathrm{~cm}$$
Question 7
1 / -0

The velocity of efflux of a liquid through an orifice in the bottom of a tank does not depend upon

A
density of liquid

B
height of the liquid column above orifice

C
acceleration due to gravity

D
None of these

Solution
Question 8
1 / -0

A large tank filled with water has two holes in the bottom, one with twice the radius of the other. In steady flow the speed of water leaving the larger hole is______ the speed of the water leaving the smaller.

A
twice

B
four times

C
half

D
the same as

Solution

Velocity of water surface,$${{v}_{1}}=0$$

From Bernoulli equation

$$ P+\dfrac{\rho {{v}^{2}}}{2}+\rho gh=\text{constant} $$

$$ {{P}_{atm}}+\dfrac{\rho v_{1}^{2}}{2}+\rho g{{h}_{1}}={{P}_{atm}}+\dfrac{\rho v_{2}^{2}}{2}+\rho g{{h}_{2}} $$

$$ \dfrac{\rho v_{2}^{2}}{2}=\rho g({{h}_{1}}-{{h}_{2}}) $$

$$ {{v}_{2}}=\sqrt{2g({{h}_{1}}-{{h}_{2}})} $$

Velocity of water is $$\sqrt{2g({{h}_{1}}-{{h}_{2}})}$$

Speed of water from hole is independent on area.

Hence, In steady flow the speed of water leaving the larger hole is the same as the speed of the water leaving the smaller.
Question 9
1 / -0

Water flows through a horizontal tube as shown in figure. If the difference of heights of water column in the vertical tubes in $$2\ cm,$$ and the areas of cross-section at $$A$$ and $$B$$ are $$4 \mathrm\ { cm } ^ { 2 }$$ and $$2 \mathrm\ { cm } ^ { 2 }$$ respectively, find the rate of flow of water across any action

A
$$126 \mathrm\ { cm } / \mathrm { s }$$

B
$$136 \mathrm\ { cm } / \mathrm { s }$$

C
$$146 \mathrm\ { cm } / \mathrm { s }$$

D
$$156 \mathrm\ { cm } / \mathrm { s }$$

Solution

$$\text { given, } h =2 \mathrm{~cm} \\$$
$$A_{1} =4 \mathrm{~cm}^{2} \\$$
$$A_{2} =2 \mathrm{~cm}^{2} \\$$
$$Acc. \text { to } \text { Continuity theorem } \\$$
$$A_{1} v_{1}=A_{2} v_{2} \\$$
$$4 \cdot v_{1} =2 \cdot v_{2} \\$$
$$v_{2} =2 v_{1}$$

Acc.to Bernoullis theorem

$$P_{0}+\rho g h+\frac{1}{2} \rho v_{1}^{2}=P_{0}+0+\frac{1}{2} \rho v_{2}^{2}$$

$$g \times 2+\frac{1}{2} v_{1}^{2}=\frac{4 v_{1}^{2}}{2}$$

$$4000=3 v_{1}^{2}$$

$$v_{1}=36.5 \mathrm{~cm} / \mathrm{s}$$

rate of flow$$=36.5 \times 4$$

$$=146 \mathrm{~cm}^{3} / \mathrm{s}$$

Answer:- $$(C)$$
Question 10
1 / -0

Consider two shoulder bags, one with a thin strap, and the other with a wide strap. If both the bags are equally heavy, the bag with the wide strap will be more comfortable to carry because

A
the thin strap has greater inertia per unit length

B
the thin strap causes greater momentum to be exerted

C
the wide strap allows friction to be spread over a bigger area, thus reducing force between shoulder and the strap

D
the wide strap enables the weight of the bag to be spread over a bigger area, thus reducing the pressure on the shoulder.

Solution

Pressure is defined as $$P =\dfrac{\text { Force }}{\text { Area }}$$

Hence, pressure is inversely proportional to area.

Since, wider strap has more area, than the thinner strap, so less pressure will be applied on shoulder.

Hence, the bag with wider strap is more comfortable.

The correct option is D.

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Mechanical Properties of Fluids Test - 47

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Mechanical Properties of Fluids Test - 47

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Question 1

$$t = \sqrt { \dfrac { 2 \sigma ( 1 + \sin \theta ) } { \rho g } }$$

$$t = \sqrt { \dfrac { 2 \sigma ( 1 - \cos \theta ) } { \rho g } }$$

$$d = \sqrt { \dfrac { 2 \sigma } { \rho g } }$$

$$d = \sqrt { \dfrac { 2 \sigma ( 1 - \cos \theta ) } { p g } }$$

Question 2

4095.0 Pascal

409.50 Pascal

40.950 Pascal

4.0950 Pascal

Solution

Question 3

$$\dfrac{{x\pi {R^2}{n_1}}}{{{n_2}}}$$

$$\dfrac{{x\pi {R^2}{n_2}}}{{{n_1}}}$$

$$\dfrac{{2\pi {R^{}}{n_1}}}{{{n_2}}}$$

$$\pi {R^2}x$$

Solution

Question 4

Bernoulli's Law

Posieulles principle

Pascal's law

Archimedes principle

Solution

Question 5

initial speed with which the water flows from the orifice.

initial speed with which the water strikes the ground and

time taken to empty the tank to half its original value.

Does the time to empty the tank upon the height of stand?

Question 6

$$0.025\ cm$$

$$0.021\ cm$$

$$0.020\ cm$$

$$0.027\ cm$$

Solution

Question 7

density of liquid

height of the liquid column above orifice

acceleration due to gravity

None of these

Solution

Question 8

twice

four times

half

the same as

Solution

Question 9

$$126 \mathrm\ { cm } / \mathrm { s }$$

$$136 \mathrm\ { cm } / \mathrm { s }$$

$$146 \mathrm\ { cm } / \mathrm { s }$$

$$156 \mathrm\ { cm } / \mathrm { s }$$

Solution

Question 10

the thin strap has greater inertia per unit length

the thin strap causes greater momentum to be exerted

the wide strap allows friction to be spread over a bigger area, thus reducing force between shoulder and the strap

the wide strap enables the weight of the bag to be spread over a bigger area, thus reducing the pressure on the shoulder.

Solution

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